Well, here's a problem I have, based solely on your description. "A rapier would be next to useless." well, since for safety sake I'm going to guess that they wouldn't be allowing a sharpened rapier, which is designed to slip between joints, seams, and chain-mail links, yeah, it might seem useless. But there's a reason plate-mail went out of fashion in favor of the rapier. And it's a lot more complicated than my trite comments make it sound. There are entire books written on the factors that lead to the changes of arms and armor.

If you find the show interesting and entertaining, that's great. I would not, however, assume that it is anything like a definitive guide or entirely accurate in the depiction of how fighting was done, any more than I would Medieval Times Dinner Theater. You're (slightly) more likely to find accurate depictions at your average Ren' Faire or SCA tournament.